关于完整Coriolis力作用下的非线性Rossby波传播的研究

发布时间：2018-03-25 01:04

本文选题：完整Coriolis力　切入点：水平分量　出处：《内蒙古大学》2017年硕士论文

【摘要】：Rossby波是大气与海洋运动的主要波动之一,是影响地球流体大尺度运动的主要波动.本文从含有完整Coriolis力的地转位涡方程出发,对非线性Rossby波的演变主要作了如下的两方面研究:一方面,考虑正压流体中纬向基本气流具有弱切变的情况,推导出非线性Rossby波包振幅满足推广的非线性Schrodinger方程.结果表明,Coriolis参数水平分量对Rossby波包产生一定的影响.同时,β效应、地形效应和耗散也是诱导及影响Rossby波包产生的重要因素.并且研究了基本气流存在线性弱切变下的本征值问题.另一方面,通过合理的赤道β平面近似,利用摄动法和时空伸长变换法,得出在地形和耗散的作用下的非线性Rossby波振幅满足的非齐次Benjamin-Davis-Ono-Burgers(BDO-Burgers)方程.通过实例说明了地球旋转水平分量和地形等对Rossby波演变的影响.取特殊情况时,结论可以退化为前人已有的的结果.
[Abstract]:Rossby wave is one of the main waves of atmospheric and oceanic motion, and it is the main wave that affects the large-scale motion of the earth fluid. In this paper, we proceed from the geostrophic vorticity equation with complete Coriolis force. The evolution of nonlinear Rossby waves is studied in two aspects: on the one hand, considering the weak shear of the basic zonal flow in barotropic fluid, The nonlinear Rossby wave packet amplitude satisfies the generalized nonlinear Schrodinger equation. The results show that the horizontal component of the Coriolis parameter has a certain influence on the Rossby wave packet. Topographic effect and dissipation are also important factors to induce and influence the generation of Rossby wave packet. The eigenvalue problem of the basic airflow with linear weak shear is studied. On the other hand, through the rational equatorial 尾 plane approximation, Using perturbation method and space-time elongation transformation method, The nonhomogeneous Benjamin-Davis-Ono-Burgersn BDO-Burgersequation for the amplitude of nonlinear Rossby waves under the action of topography and dissipation is obtained. The effects of the horizontal components of the earth rotation and topography on the evolution of Rossby waves are illustrated by examples. The conclusion can degenerate into the previous results.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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